# Liquidity for Alternative Risk Transfer Instruments: ILS use case for AMM

**Abstract:** Recently, cryptocurrency-based Automatic Market Makers such as [Balancer](https://balancer.fi/),[Uniswap](https://uniswap.org/) and [Curve](https://curve.fi/) have received significant attention, as well as millions of dollars in liquidity. At first glance, such AMMs do not seem well-suited to risk-averse traditional finance instruments like Insurance-Linked Securities. However, we show that these markets can actually offer a straightforward mechanism for providing a secondary market for tokens which serve as virtual representatives of an ILS.

## What are Insurance-Linked Securities?

An Insurance Linked Security is an alternative risk transfer (“ART”) instrument. Its purpose is for investors to be able to take on risks in a way that does not require them to be a regulated insurance / reinsurance company. Risk Transfered is effective in all circumstances. The extent of risk transfer is clearly defined and incontravertible.

**ART instruments have clear regulatory requirements:**
* Assets must be valued in accordance with IFRS or UK GAAP.
* Insurance Special Purpose Vehicle must at all time.
* Have assets which equal or exceed the aggregate maximum risk exposure and
* Be able to pay amounts as they fall due.
* Proceeds of debt issuance must be fully paid-in.
* Cannot use contingent assets.

Investors are rewarded for the risk they take on. The reward is inform of a cupon/ dividend/ return.

## Opportunity for DeFi
An ART instrument is issued inside an Insurance special purpose vehicle (ISPV)/ Risk Transformer Vehicle. An ISPV has separate cell for each risk transfer contract. These cells have segregated pool of assets and liabilities (record-keeping). Each cell is insolvency-remote from each other cell. Investors in cells confined to non-voting securities.This container structure and associated regulation makes this asset and ideal contender for tokenisation.

Tokenisation in this context refers to the process of utilising blockchain technology to mint a Token/ Tokens. A Token is a homogenous, digital unit represenstation of the collateral ownership. Value of the token is a function of the collateral. We further classify this token based on HMT & FINMA guidance as a "security token".
The security token arrangement comprises of various technology stacks working together to enable

## Issuing ART Tokens
Our mission is to create a functional Insurance capital infrastructure for Investors and Insurers alike. This involves a hybrid model of execution where ART assets are minted in an mISPV post creation an Non Fungible Token counter party contract. ILS and may wish to sell foe cryptocurrency. We issue a virtual ILSx token with the following properties:
1. At a fixed future date, each ILSx can be redeemed for 1 USD or USDC if there has been no payout event
2. At regular intervals, each address holding an ILSx token will receive coupon payments denominated in a stablecoin such as DAI or xDAI. (I think we need to use DAI or xDAI here since the addresses we have will be Ethereum addresses.)

Unlike much of cryptocurrency, we make no pretense of decentralization, trustlessness, etc. This is a centralized instrument whose value depends on our commitment to provide the specified value at a future date.

## Basic Pool Design for ILSx tokens

One design for the purpose of providing a market could be achieved as follows: a constant sum Automatic Market Maker with the equation
$$x + y = k$$

where $x$ is the balance of ILSx tokens, $y$ is the balance of our stablecoin of choice (e.g. USDC), and $k$ is the number of ILSx tokens issued to the pool. This equation maintains a constant price of 1 ILSx/USDC, with the balance of ILSx guaranteed to never exceed the initial issuance amount.

The pool will grow in value (in USDC) by charging fees (in USDC) for each transaction. We would recommend taking these fees to a separate account, since we do not want the value of $k$ to increase -- this could potentially be exploited to increase the number of ILSx tokens beyond our actual supply.

## Potential Drawbacks to the Basic Pool Design

It may not be attractive to ILSx token holders to only be able to sell their tokens at a fixed value of 1 USDC, when market forces may drive the value higher.

A highly flexible pool design could be implemented of the form
$$ a(t)x + b(t)y = k(t) $$
where $x$ is the balance of ILSx tokens, $y$ is the balance of USDC (or other stablecoin), and $a(t)$, $b(t)$, and $k(t)$ are functions of time. This is a dynamically weighted constant-sum market maker, whose properties will depend heavily on $a(t)$, $b(t)$, and $k(t)$. For instance, we may choose the functions $a$, $b$, and $k$ to gradually decrease the price of 1 ILSx as the coupon payments are issued and future value decreases.

## Trigger Events

**It is important to note that the collateral which would be used to pay a claim is never placed in the cryptocurrency pool.** However, a trigger event would still need to be reflected in our cryptocurrency pool, since it will adjust the price of our ILSx token.

We can adjust the price in the pool by moving from the equation
$$x + y = k$$

to

$$x + py = k$$ where $p$ is the proportion of returnable collateral remaining.

For instance, if our collateral is 10000 USD to be returned to investors upon reaching the term of the contract, but a trigger event claims 1000 USD, we now only have 9000 USD to return. Accordingly, if we released 10000 ILSx tokens initially, each one should only be worth 0.90 USDC upon payout for the trigger event. We would adjust the constant-sum equation in this instance to

$$x + 0.9y = 10000$$

which maintains the desired price.

The dynamics of this are potentially problematic vis-a-vis communication and timing. If the trigger event is publicly known, any ILSx token holders will want to sell their tokens back before any price adjustments, and our AMM will be obligated to take them back. One option would be to pause the pool as soon as a claim is initiated, pending processing of the claim.

## Risks

The major risks in this pool design lies in the stability of the stablecoin paired with the ILSx token.

**Normal Variability:** Since USDC hovers in a range around 1 USD, there are times when the value of the ILSx pool will be lower than the promised payout, which would mean a loss of value (demarcated in USD). However, the nature of USDC means that the value is likely to at some point rise again.

**Stablecoin Collase:** In the event of a complete stablecoin collapse, where the market value of our chosen stablecoin falls far 1 USD and is unlikely to ever return. The true risk of this event is impossible to gauge, but this risk seems instrinstic in nearly all cryptocurrency investments involving stablecoins.

## Potential Extensions

It is tempting to modify our simple proposed ILSx-stablecoin pool to attract a higher trading volume.

One option would be to add a second stablecoin, e.g. creating an ILSx-USDC-DAI pool, with USDC-DAI trading fees generating income for the pool without affecting the price of the ILSx token. This increases the risk, as the phenomenon of impermanent loss is almost guaranteed to lower the USD value of the USDC-DAI portion of the pool.

We have two types of traders interacting with the pool
(1) Arbitrageurs - profit-seeking agents aiming to close arbitrage gap between this AMM and some other (external) market
(2) Organic Traders - agents, that use the pool for their own trades. These agents even could not know about existence of your pool since they use 1inch which routes trades via several different pools (including yours in our example). All who are not arbitrageurs fall in this category.

## Questions for Analysis and Simulation

1. What is the incentive for traders to purchase ILSx tokens from our secondary pool?
2. How vulnerable is the ILSx-stablecoin pool to loss of value from the stablecoin? Are trading fees likely to cover the small fluctations in stablecoin value?
3. Are there any advantages to dynamic weights modifications of our basic ILSx-stablecoin pool design?
4. How should pool adjustments in response to a trigger event be handled?
5. Is it possible to create a useful hybrid between our risk-averse ILSx-stablecoin pool and more tradtional AMMs?